Physics 1A
Lecture 3B
"It is good to have an end to journey towards, but it
is the journey that matters in the end."
-- Ursula K. LeGuin
Quiz 1 Info
Date of Quiz: Jan. 23rd, in class.
It will be a Scantron test covering Chapters 1, 2, and 3.
A list of equations will be provided on the quiz.
You are to write the version of your test on the Scantron
form.
You will be given a Quiz Code Number that you will be your
Quiz ID for the rest of the quarter.
You are expected to abide by UC Policy on Integrity of
Scholarship.
2-D Variables
Average acceleration is again the change in
velocity over the time interval:
Since Δt is a scalar and always positive,
average acceleration will always point in the
direction of the change of velocity.
Instantaneous acceleration is again the
acceleration of an object at any instant of time.
Kinematics Equations
The kinematics equations that we learned for
one dimensional motion (when a = const) still
hold when we increase to two dimensions.
But the equations apply separately to each
component of two dimensional motion.
BIG PHYSICS CONCEPT!!!!!!
Horizontal and vertical motion are independent
of one another.
Neither motion affects the other.
Kinematics Equations
This means that if there is an acceleration in the
y-direction; it will not affect motion in the
x-direction at all.
So for motion in two dimensions you can use the
following equations as long as ax and ay are
constants.
Kinematics Equations
Note that we have subscripts now denoting
variables that are in the x and y directions.
Also note that time has no subscript. It is the
one link between the two sets of equations.
Projectile Motion
An object that moves in a gravitational field, in
both the x and y directions simultaneously is
said to have projectile motion.
With projectile motion we are assuming that
air friction is negligible.
An object
following
projectile
motion will
follow a
parabolic path.
Projectile Motion
Typical Projectile Motion Problem
A cannonball is shot at a given angle (30.0o)
with a certain muzzle velocity (100m/s). How
far from the cannon does the cannonball
land?
Answer
First, you must define a coordinate system.
Let’s choose the upward direction as positive
in the y-direction, and the horizontal
direction the cannonball travels as the
positive x-direction.
Projectile Motion
Answer
To handle, separate into
two problems (x and y).
First, break velocity into
components.
Projectile
Motion
Answer
Now, use the kinematics equations separately in
each direction.
First, let’s try the x-direction.
Let’s list the quantities we know:
vox = +86.6m/s
ax = 0m/s2 = constant <-- no acc. horizontally
vx
<-- don’t know
Δx
<-- finding
t
<-- don’t know
Let’s try the third equation:
Projectile
Motion
Answer
That didn’t help us much, one equation with two
unknowns.
What about the other three kinematics
equations for the x-direction (with ax = 0)?
We should turn to the y-direction.
Projectile
Motion
Answer
Now, let’s try the y-direction.
Let’s list the quantities we know:
voy = +50.0m/s
ay = -9.80m/s2 = constant
vy
<-- don’t know
Δy = 0
<-- falls to same height
t
<-- don’t know
What is the one variable we can solve for in
the y-direction and place in the x-direction
equations?
time, t: so we are now finding time.
Projectile
Motion
Answer
Looks like it’s the third equation for us.
t = 0 represents when the ball was first shot.
t = 10.2 sec is the time is takes to hit the ground.
Projectile
Motion
Answer
We input this time into the x-direction equations:
This is the horizontal distance travelled by the
cannonball.
Other typical questions asked are:
How high does it go?
How long is it in the air?
In class Question
A cannonball is shot from a cannon at an angle of
30o with respect to the horizontal. Which of the
following choices is correct concerning the resulting
projectile motion?
A)
B)
C)
D)
E)
The
The
The
The
The
speed is zero at the top of its path.
speed is a maximum at the top of its path.
speed is a minimum at the top of its path.
acceleration is zero at the top of its path.
speed is 9.8 m/s at the top of its path.
Projectile Motion
At any point in the path of a projectile, the
projectile’s velocity (magnitude) will be:
And the angle
it makes with
the horizontal
will be:
Projectile Motion
Checklist for handling projectile motion problems:
1) Break appropriate vectors (position, velocity,
acceleration) into components (if not already).
2) Use the appropriate kinematics equations
separately in the x and y directions.
3) Substitute common information to the other
equations to solve for the appropriate variable.
4) If you need to transfer information between
the x and y directions, most likely time is the
appropriate variable.
For Next Time (FNT)
Finish Chapter 3 HW.
Study for Quiz on Friday.
Start Reading Chapter 4.